Let \({{D}\mathrm {fg}}\)  denote the category of diffeological spaces as defined in [1]}—this is the full subcategory of \({{C}\mathrm {at}}({{C}\mathrm {art}}^\mathrm {op}, {{S}\mathrm {et}})\)  on the concrete sheaves with respect to the Grothendieck pretopology \(\tau \)  (see the beginning of Section REF ).
Concretely, a diffeological space can be defined as a pair \((X, \mathrm {Plot}_X)\) , where \(X \in {{S}\mathrm {et}}\) , and where \(\mathrm {Plot}_X\)  assigns to every cartesian space \(c \in {{C}\mathrm {art}}\)  a subset \(\mathrm {Plot}_X(c) \subset {{S}\mathrm {et}}(c,X)\)  of the maps from the underlying set of \(c\)  to \(X\) .
These maps are called plots of \(X\) and have to satisfy that
